Vacancy-interstitial pairs in ordered smectic phases : a linear Guinier-Preston zone behaviour

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Vacancy-interstitial pairs in ordered smectic phases : a

linear Guinier-Preston zone behaviour

A.M. Levelut

To cite this version:

1517

Vacancy-interstitial pairs

in ordered smectic

_{phases :}

a linear

Guinier-Preston zone behaviour

A. M. Levelut

Laboratoire de

Physique

des Solides, Bâtiment 510, Université Paris-Sud, 91405

_Orsay

Cedex, France

(Reçu

le 1er

_février

1990,

accepté

le 21 mars

₁₉₉₀₎

Résumé. - Les clichés de diffraction obtenus

sur des monodomaines de

phases smectiques

B et G

présentent

une succession de

lignes

contrastées

_parallèles

et

_{équidistantes,}

une

_ligne

centrale blanche étant associée à une série de

_lignes

noires de même forme. On montre _que ces

_lignes

forment la

_signature

d’un défaut linéaire constitué d’une lacune moléculaire entourée d’un interstitiel délocalisé sur dix à

_quinze

sites. La

présence

de tels défauts met l’accent sur le caractère tridimensionnel

_périodique

de

_{l’organisation}

dans ces

_phases.

Nous discutons des

relations de ces défauts avec le désordre orientationnel moléculaire ainsi que de leur influence sur

les

_{propriétés élastiques statiques}

et

_dynamiques

de ces

_systèmes.

Abstract. - An

original

diffuse

_{X-ray scattering}

_pattern is observed for

_single

domains of

three-dimensionally

ordered Smectic B and G

phases :

a

_{fairly sharp}

white line

_{going through}

the center

of the

_reciprocal

space is associated with a

_periodic

set of

_parallel

and

_equidistant

black lines of similar

_shape.

It is demonstrated that this set of lines is the

_signature

of a linear defect

_consisting

in a localized vacancy surrounded

by

a delocalized interstitial. As a matter of fact such defect

display

the

_{crystalline properties}

of the Smectic B and G

_phases.

The relation between these defects and the molecular orientational disorder as well as the consequence upon the static and

dynamical

elastic

_properties

of these

_phases

are discussed.

J.

_Phys.

France 51

₍₁₉₉₀₎

1517-1526 15 JUILLET 1990,

Classification

Physics

Abstracts

61.30 - 61.70B - 61.70Y

During

the last decade the structural studies of ordered smectic

_phases

have been focused

on the

_problem

of the

_phase

transitions from a 3D

_crystal

towards a two-dimensional network.

In

_fact,

a well established classification

_[1]

_]

of these

_mesophases

in two _{groups makes the} distinction between the

_{mesophases organised}

in stacked

_layers,

in which the molecules form

a two-dimensional

_periodic

array

(SmF

SmI and hexatic

_B),

and the

_mesophases

which

_keep

a

three-dimensional

_crystalline

character in

_spite

of the

_{high degree}

of molecular orientational

disorder

_(crystalline

_{SmB, SmG, SmH,}

_etc.).

For the _{first group of}

_mesophases

a

fairly

coherent

_description,

based on the theoretical

_predictions

about 2D

_melting

and on a

comparison

with various

_experimental

_data,

is now available

_[2].

The second group of

mesophases

can be considered as

_belonging

to the class of the

_{orientationally}

disordered

molecular

_crystals.

_However,

the

_mesogenic

character of these

_systems

can be found in their

lamellar

_properties

and in the

_polymorphism

of the molecules

involved,

since in

general

such molecules

_undergo

several

_{mesophases. Keeping}

off any semantical

problem

we have

attempted

to progress in a

_complete

characterization of the

_ordering

in these so-called

_liquid

crystalline phases.

The existence of a mean 3D lattice cell and its

_symmetry

_properties

in relation with the nature of the

_mesophase

have been established with earlier structural studies

[3]

and no doubt remains on this

_point.

However,

the disorder which can be more

_precisely

described in terms of

fluctuations,

motions and defects takes a

_predominant

_part.

Each

component

of the disorder is

_generally

understood alone and a

_{comprehensive approach}

has not

_yet

been

_attempted.

Here we

_present

a first tentative

_step

restricted to the

_crystalline

SmB

₍₁₎

and SmG

_mesophases

and based on a new

_approach

of some features of the diffraction

_patterns

which we had

_{already analysed}

in detail in our

_previous

_papers.

Let us first describe the

_experimental

conditions _very

_briefly

and then

_give

a short summary

of our

_previous

conclusions.

The

_{diffraction experinients}

are carried out either on

_single

domains obtained

_{(by heating)}

from

_{single crystals}

or on fibers obtained

_by

slow

_cooling

of Smectic A

_{samples aligned by}

a

magnetic

field. The monochromatic and

_{point focusing X-ray}

beam is issued from a

_Bragg

reflection on a

_doubly

curved

_single

LiF

_crystal

or on a

_{pyrolitic graphite.}

The scattered

X-rays are collected on a

_{photographic plate}

and

_generally

we

_keep

the

_sample

in a fixed orientation.

_Figure

1

_presents

a few

_examples

of these diffraction

_patterns.

For one of them

(Fig. la)

the director is

_{nearly parallel}

to the

_X-ray

beam while in all the others the director is almost

_{perpendicular}

to the

_X-ray

beam.

The 3D

_{crystalline properties}

are confirmed

by

the

_Bragg

reflections which form a 3D

reciprocal

network of

_sharp,

resolution

limited,

peaks ;

the lattice cell is monoclinic

_(SmG,

Figs.

lb,

lc)

or

_{hexagonal (SmB, Figs.}

_Id,

_{le) [3, 4].}

The

_spots

of measurable intensities are

all localized in a central zone of

_reciprocal

_space bounded

_by

a

_{prolate ellipsoid.}

The size of

this

_ellipsoid

characterises the amount of

_positional

fluctuations

_throughout

an

_anisotropic

Debye-Waller

factor.

In our

_{previous publications}

we have

_{distinguished}

two kinds of fluctuations :

_firstly,

the usual

_phonons

scattered

_X-ray

in broad zones with a maximum of

_intensity

near the

_Bragg

peaks

(centers

of the Brillouin

_zones)

and

_secondly,

some fluctuations which are due to

anisotropically

correlated « disorder » and

_correspond

to the scattered

_intensity

localised at

specific points

of the

_reciprocal

lattice. We have

_{mainly brought}

our attention to this second kind of disorder : in the

_{equatorial plane perpendicular}

to the

director,

diffuse

_spots

_sitting

at

specific points

of the Brillouin zone

_boundary

form,

with the

_Bragg

reflections on the

pseudo-hexagonal

lattice

_planes,

two-dimensional

_rectangular

networks of lower

symmetry

corre-sponding

to a

_herring-bone

_{local array of the}

_elliptic

cross sections of the

molecules ;

three

different orientations of such domains coexist in order to

_keep

the mean

pseudo-hexagonal

symmetry.

It has been shown that the

_herring-bone

array results from correlated rotational

motions of the molecules around their

_long

axes

_[5].

A

_part

of the diffuse

_X-ray

_intensity

is also localised in

_{non-equatorial}

_{reciprocal lattice}

planes perpendicular

to the director. This

_intensity

is therefore issued from some

_periodic

linear defects

_parallel

to the director. These defects are

obviously

related to the 3D character of the SmB and SmG

_{phases [6].}

In

_fact,

the diffracted

_intensity

of the

_{Bragg peaks}

_represents

_only

a small

part

of the whole

scattered

_intensity.

Therefore it is clear that much disorder is still there in ordered smectic

phases, consequently

a

_description

of this disorder in

independent

fluctuations cannot be

realistic. The

_coupling

between two kinds of fluctuations will induce interferences in the

scattered

_intensity

and interferences

_imply

addition as well as subtraction of

_amplitudes

of

1519

Fig.

1. -

X-ray

diffraction pattern of SmB and G

_{phases (JICuKa radiation).}

Various films to

_sample

distances.

_{a) Terephthal}

bis

_butyl

aniline

_{single crystal}

heated at T = 120 °C. The director is

nearly

parallel

to the

X-ray

beam.

b)

Terephthal

bis

_butyl

aniline

_{single crystal}

heated at T = 115 °C. The director is

_{nearly perpendicular}

to the

_X-ray

beam.

_c)

p

butyloxybenzylidene p’ethyl

aniline

(40.2)

single

crystal

heated at T = 50 °C. The director is

perpendicular

_to the

X-ray

beam.

d)

_p

phenylbenzylidene

p’butyloxyaniline

single crystal

heated at T = 90 °C.

e)

_p

butyloxy benzylidene p’octyl

aniline

(40.8)

fiber

_aligned

in a

_magnetic

field T = 51 °C.

It is clear that all the

_patterns

shown in

_figure

1 exhibit white

_sharp

lines _{among grey} zones.

These lines are

_clearly

visible in the

vicinity

of the

_Bragg

hk0 reflections

_(issued

from the

hexagonal array)

where

_they

are extended in a

_longitudinal

direction

_{(Fig. la).}

Another white

a _grey zone which covers the central

_reciprocal

unit cell. This white line is _present in the diffraction

_pattern

of SmG and SmB

phases

either on

_single

domains obtained from

_single

crystals ( 1 b-d)

or on fiber

_{samples aligned by}

a

magnetic

field

_(le).

The

_shape

of the line is

slightly

different for SmG and SmB. In the first case the line is extended close to the first

Bragg

peak

100

_{(characterising}

the

_{hexagonal lattice)}

and its width is constant. For SmB the line is rather

_sharp

at the center of the

_reciprocal

space, but becomes wider as the

_scattering

vector increases in

_length.

In both cases black lines of similar

_shapes

and directions are seen

going through

the

00i

_Bragg

reflections on the

_{layer planes.}

Therefore black and white lines

are

_likely

related to the same structural feature. Let us first consider the

_simplest

case of

_sharp

straight

and narrow lines. The existence of a

_strong

contrast in the diffuse scattered

_intensity

at the center of the

_reciprocal

_{space is}

_necessarily

related to

_density

fluctuations. In the absence of a central white

_line,

the broad _grey band would be induced

_by

a defect which has the form factor of a molecule such as a

_single

_{vacancy. As} was

_{previously explained, sharp}

dark lines are sections of

_{reciprocal planes perpendicular}

to the director and

_correspond

to

lines of molecules

_being

out of

_phase

with the mean

_crystal.

_However,

the scattered

_amplitude

will be non-zero at the center of the

_{reciprocal only}

if the defect has an electronic

density

which is different from that of the mean

_crystal.

If vacancies and linear defects are not correlated in

_position

the intensities scattered

_by

the two defects added at each

_point

of the

reciprocal

space ; in contrast, if

_they

are correlated we must consider a

_unique

defect made of

two

_parts

and we have to

_apply

an addition rule for the scattered

_amplitudes

of the two

_parts.

Intensity profiles

going similarly

from zero for the center of the

_reciprocal

space to a

maximum value for an

_angle

of about 1 0

and then

_{decreasing slowly}

for

_{larger angles}

have been

put

in evidence in small

_angle

_X-Ray

_{scattering experiments}

carried on aluminium

_alloys

containing

a small amount of

_Zn,

studied

_during

the first

_steps

of the

_{decomposition}

into two

phases [7].

The defects which are at the

_origin

of such small

_angle

diffuse

_scattering

halo are

known as Guinier-Preston zones

_{(GP zones).}

Such defects have been

_previously

described as

the association of two coherent zones of different electronic densities : the central

_part

is a

cluster of

_impurities

surrounded

_by

a

_depletion

crown free of

_impurities.

The number of

foreign

atoms in the central area of the cluster is

_equal

to the number of the same atoms that

were

_previously

_present

in the total volume of the

_defect,

when

_impurities

were

_randomly

dispatched.

At zero

_{scattering angle,}

the diffracted

_amplitude

is the addition of two terms

which have the same

_value,

but

_{opposite signs ;}

because of the difference of

size,

the two terms decrease with a different

slope, consequently

the width of the diffuse

scattering

band

depends

on the ratio between the sizes of the two

_components

of the defect. Let us remark

that the

_analysis

which was

_{quickly reported}

above holds for

_{randomly dispatched}

GP zones,

while in

_{general they}

cover

_nearly

the whole volume. A better

_description

of the first

_stage

of

clustering

in solid solutions

_quenched

at room

_temperature

has been

_given

_by

Cahn in a model

in which the

_{spinoidal decomposition}

of the

_alloys

induces a

_quasi

sinusoidal

_spatial

_profile

of the

_impurity

concentration

[8].

Experimentally,

GP zones have concentration

_profiles

which

are anharmonic since the first

ageing

_stages,

and the

previous description

of GP zones remains

valid in

_spite

of the fact that some

_points

are still obscure in their structures

_{[9, 10].}

In SmB and G

_phases

the

_{small-angle scattering intensity profile}

is

_anisotropic

since it

depends only

on

the f

coordinate of the

reciprocal

_space

(perpendicular

to the smectic

planes) ;

moreover it is

strongly

anharmonic in a direction

_parallel

to the director. This

anharmonicity

excludes any idea of a

_quasi

sinusoidal fluctuation. The absence of a

pronounced peak

in

_intensity

for

_h,

_A:,

_1,

_implies

that the defects are

_{randomly dispatched}

in every direction.

Finally

the

_sharp

contrast between the narrow central white band and the

surrounding

grey band of rather uniform

intensity

allow a

_{straightforward}

estimation of the

1521

molecule while the whole defect is

_linear,

_parallel

to the

_director,

with a

_{length proportional}

to the inverse width of the white zone. Therefore the association of a

_single

_vacancy

surrounded

_by

a linear zone

_parallel

to the director

_containing

one molecule in excess

_(by

.

comparison

with the «

perfect

»

areas)

forms the GP zone

responsible

for both the small

angle

scattering intensity

and the dark diffuse lines. Let us remark that the reverse situation of a

single

interstitial surrounded

_by

a delocalised vacancy, while

fitting

well with our

_experimental

results,

is unrealistic if the distortion induced

by

a localised interstitial is taken into account.

The amount of such defects has not been measured since we have not

_performed

absolute

intensity

measurements of the

_{small-angle scattering background. Anyway,}

we can estimate that there are at least 1 % of

_single

vacancies in order to

_give

a

_background

of somewhat

higher

diffuse scattered

_intensity

than that induced

_by

the

_{longitudinal phonons}

at zero

_angle

[11].

The structure of the defect can be described

_by

various models.

The

_simplest

one

_corresponds

to a diffuse interstitial which is not localised at a

_given

position.

Let us consider a defect made of

_{(2 n + 1 )}

molecules of structure factor

Fo.

In the undisturbed structure the molecules are

_aligned

with a

_repeat

vector c. If the

interstitial is not

_{localised, the central site is the vacancy and the n molecules}

_sitting

on each

side are not

_displaced,

but their structure factor is enhanced

_by

a ratio

(2 n

+

_1)/2

n. Since the lattice is

non-distorted,

the

_{intensity profile}

will be

_{repeated identically}

at the center of the

reciprocal

space and around each

OOf

Bragg

peak.

Such a model does not fit with our data and

in fact the idea of a diffusive interstitial is

_opposite

to the idea of a finite

length

defect. The

molecule in excess is more

likely

inserted in a line of N molecules

inducing

a

_shrinking

of the lattice

_{spacing by}

a factor

N/N

+ 1. We have considered two

_positions

for the central vacancy :

i)

the vacancy is centered between two lattice

sites,

and the defect contains an even number

of molecules 2 n, n molecules

being periodically dispatched

on a

length (n -1/2)

c

(Fig. 2a) ;

ii)

the vacancy is centered on a lattice site and the defect contains an odd number of

molecules 2 n + 1. For

_symmetry

_reasons, we admit that n +

_1/2

molecules are

_dispatched

on

n sites on each side of the vacancy. At each end of the defect, a

_molecule,

shifted of half a

period,

is shared

_by

two

_adjacent

defects and successive defects of the same raw

_parallel

to c are of random

_{length (Fig. 2b).}

Fig.

2. - Models for the linear

vacancy-interstitial pair : a)

the central vacancy is shared

by

two

_{layers ;}

b)

the central vacancy is centred in a

_layer.

Figure

3 shows the diffracted

_intensity

obtained from the last two models for 0

f

1.8 c*.

Around f

=

0,

the white band is

clearly

observed. Around f =

1,

the

intensity

profile

presents two minima of

_{inequal depths surrounding}

a maximum. The

sign

of this

asymmetry

is different for the two kinds of defects and its

_amplitude

varies with f. A similar behaviour has been

_already

seen in aluminium

_alloys

where the

disymmetry

in the

_intensity

profile

around the different

_Bragg

_peaks

is

_{explained by}

the distortion of the

_impurity

rich

Fig.

3. - Calculated small

angle

diffuse

_{scattering intensity (in}

molecular structure factor

units)

versus

the

reciprocal

coordinate 1

parallel

to the director.

a)

The vacancy is shared between two

_layers.

The

intensity corresponds

to a mean value over 6 defects of

length

2 n with

(n

=

4)

_x 1,

(n

=

5 )

_x 2,

(n

=

6 )

_x 2,

(n

=

7 )

_x 1.

b)

The vacancy is centered in _a smectic

layer.

The

intensity corresponds

to _a

mean value over 9 defects of

_{length (2 n}

+

_{1 )}

layer

thickness with

_(n

=

3 )

x 1,

(n

=

4 )

_x 2,

(n=5)x3, (n=6)x2, (n=7)x

1.

In

_figure

3 we have not taken the molecular structure of the

_{liquid crystalline phase}

into

account. The measured

_intensity

must be

_{multiplied by}

the molecular form factor which

decreases

_quickly

for f r.-

1 and therefore

_strongly

modifies the

_{intensity profile.}

Nevertheless

it is

_clear,

at least for the diffraction

_pattern

of TBBA

_{(Fig. 1 b),}

that the first dark line is followed at

_{higher angles by}

a white one,

corresponding

thus to a defect with a vacancy

sitting

in the center of a smectic

_layer.

Our model does not take into account a

_possible

interaction of the linear defect with the

_surrounding

molecules. For the Smectic G

_phase,

the white and the

grey lines are

_laterally

extended over

_nearly

the whole

_reciprocal

lattice cell.

Therefore,

the

defect is

_strictly

linear. For the Smectic B

_phase

the lines are restricted to a central zone of about one third to one half of the lattice cell.

Moreover,

the line is

_{strongly pinched}

at the

center while the

_edges

are wider than the center. The linear defect interacts with the first shell of

_surrounding

molecules. The double

_{wing shape}

of the white or dark diffuse lines is more

pronounced

in the case of 40.8

_compound

which

_presents

a

_{hexagonal P63/M}

m c

_symmetry

(hexagonal

compact

stacking) [ 13]

than for the SmB

_phase

of the second

_compound

which has

indeed a monoclinic

_symmetry

with a tilt

_angle

of 96° . We can consider that the

vacancy-interstitial

_pair,

since it introduces an extra

_site,

acts as a small

_(the

smallest

_possible)

1523

distorted zones

_surrounding

this

_loop.

A similar diffuse area has

_already

been observed in the SmA

_phase

of some comb-like

_{polymers [14].}

The

double

_wing

_shape

of the lines varies with the ratio of the stress to the shear elastic moduli of the

_{layers :}

the more

_straight

the diffuse

lines,

the

_higher

this ratio.

_Moreover,

because of the

_{h.cp. packing}

of the

molecules,

the

complex

interstitial cannot be

_strictly

linear in the SmB

_phase

of 40.8.

Independently

of the

_stacking

mode of the

_layers,

the

_coupling

between these defects and the other fluctuations

_existing

in the SmB and SmG must be

_{significant owing}

to the

_high

concentration of vacancies. The areas

connecting

two domains of

_rectangular

_symmetry

and with a different

herring-bone

molecular

packing

are

_likely

to be sources of vacancies : the volumes

_occupied

_by

two molecules

_sitting

on each side of the

boundary

can

_intercept

themselves in such a _{way that} one of the two molecules must diffuse out of the

_layer.

The influence of the uniaxial rotational motion of the molecules on the _vacancy concentration _may

explain why

it is not

_{strongly dependent}

on the

compound

studied,

or on

_{sample preparation}

methods either. A

_typical

size for a

_{herring-bone rectangular}

domain is five lattice

_spacings

[15] ;

since,

with the

_assumption

of a

_{sharp boundary,}

about

_fifty

_per cent of the molecules

belong

to the

boundary

between two

_domains,

a _vacancy amount of 1 % of the total number

of molecules is not

_really

excessive. If the vacancy interstitial

pairs

are induced

by

the

correlated rotational motions of the

_molecules,

their residence time on a

given

site should be

comparable

to the lifetime of a domain of local

_rectangular

_symmetry.

This lifetime has

already

been measured

_by

coherent inelastic neutron

_{scattering experiments [ 15] :}

it is of the

same order of

_magnitude

(10- Il

_s)

as the characteristic time for the rotation of a

_single

molecule

_[16],

and therefore the residence time of a

single

_{vacancy has the} same order of

magnitude.

In order to

_explain

our diffuse

_scattering

pattern,

we must admit _{that the vacancy}

moves with its

joined

interstitial. Let us remark that the vacancy interstitial

pairs

must distort the

_hexagonal

lattice

_driving

to an

_asymmetry

of the

_{scattering intensity}

around the

_Bragg

peaks

[ 17]

but a linear defect extended over 10-15 molecules and

_moving

so

_quickly

must be

more

_{likely coupled}

to

_phonons

than to static distortions. The white lines seen in the

vicinity

of the hk0

_Bragg

_{peaks (Fig. la)}

can be related to a

_coupling

of these defects with

longitudinal

phonon

modes

_propagating

in a

_{plane perpendicular}

to the director. For the SmG

_phase

of TBBA these

_phonons

have also been measured in reference

_[15];

their

_frequency

has the

correct order of

_magnitude

in the whole Brillouin zone

(less

than 0.5

THz).

However no

contrast inversion

_{(corresponding}

to the white lines of the

_X-ray

_experiments)

is detected in

our

_triple

axis

experiments.

In fact the resolution of the device and the mosaic

_spread

out of the

_single

_crystal

do not allow a

_good

_{accuracy for the direction of the}

_phonon

wave vector

and

_{phonons inducing}

normal

_positive

_peaks

are

_{always superimposed}

on the

_expected

negative

one.

One can ask if the interactions between the defect and the

_surrounding

_matrix are

_only

limited to this

_coupling

with

_longitudinal

acoustic

_phonons.

The lamellar character of the smectics in

general

may have an influence on the behaviour of the transverse

_phonons

of wave

vector

_parallel

to the

_{layer planes.}

In our

_{previous description}

of the local order in SmB and

SmG,

we have underlined that the scattered

_intensity

localised in

_{reciprocal planes}

perpendicular

to the director is induced

_by

uncorrelated lines of molecules

_undergoing

a

longitudinal displacement

out of their mean

_{position [6].}

If the transverse

_phonons

of wave

vector

_{perpendicular}

to the director are

_specially

_soft,

the motions of the molecules are

_poorly

correlated between the lines

_parallel

to c. In

_fact,

the existence of the white central line cannot

be taken into account

_by

an

entirely displacive

disorder.

Therefore,

we have to reconsider our

interpretation

of the linear disorder in Smectics B and G. It is clear in

_figures

1 b and 1 c that the dark and white lines are _{very similar and} therefore the linear disorder

_{corresponds only}

to

width and

_disappear.

The array of the molecules in the defects is not

_periodic,

as in our

model,

but the distance between two molecules is

_{Zj + 1 - zj}

= _{co - 8 c exp -}

ez

where e

is the

penetration

depth

of a localised deformation of the

_layers.

The

_problem

is

_slightly

different for SmB

_since,

in

fact,

two kinds of diffuse

_scattering

lines

_{going throughout}

the 00f

_Bragg

peaks

are seen. This difference is

particularly

clear for 40.8 : the vacancy interstitial

pairs

have

an

image

made of

sharp,

double-wing-shaped

lines,

the

_first,

second and fourth orders are

visible ;

in fact broader lines which are extended over the whole

_{reciprocal lattice}

cell are also seen. These lines have a

nearly

constant width but

_they

are not

_straight,

their

_concavity

is turned towards the center of the

_reciprocal

_{space. The}

_first,

third and fifth orders are of

_high

intensity

while the even orders are not visible. In our

_{previous analysis}

_{of 40.8,}

we have

_only

taken into account these second series of

_{planes ; they correspond}

to a

_displacement

correlated

_only

on a short

_{length (two molecules). Taking}

into account the

_strange

dependence

of the intensities versus

f,

it seems that the

_displacement

is not a mere translation

of the

molecule,

but more

_likely

a reorientation _up or down of the director. This reorientation

induces a scattered

_{amplitude proportional}

to the

_{antisymmetrical}

_component

of the

electronic molecular

_density

_profile.

Therefore this effect is

_expected

to be seen

_only

for

disymmetric

molecules ;

moreover we can discriminate between the

_{antisymmetrical}

and the

symmetrical

components

by

a

_comparison

of the intensities scattered in the

_Bragg

peaks

and

in the diffuse

_planes.

In 40.8 the

_{paraffinic sublayer}

extends over half of the total

layer

thickness and the

_{antisymmetrical}

component

of the electronic

density

will be centered around

_c/4

and 3

_c/4,

thus

_explaining

the

_strong

odd even effect _upon the scattered

_intensity.

Even if the orientations

_(up

or

_down)

of

_neighbouring

molecules appear to be correlated

mainly along

the

_director,

the interactions between next

_neighbours

in a

plane perpendicular

to the director must also be taken into account. As we have

already pointed

out

_above,

the

h.cp. packing

is not consistent with

_strictly

linear interactions and the

_bending

of the

planes

of localization of the diffuse

_{scattering intensity}

_suggests

more

_complex

interactions.

However,

if

we want to _go

_further,

the

_problem

of

_building

realistic models of

_systems

that

_undergo

a

_great

amount of fluctuations is connected to the

_problem

of a

description

of the

coupling

between

these fluctuations and of the relations that link the different kinds of fluctuations to the various features of the diffraction

_pattern.

In

_conclusion,

a better

_analysis

of the diffraction

_patterns

of SmB and SmG

_phases

drive us

to

_give

a better

_description

of some linear defects

_specific

of a three-dimensional

_crystalline

phase. Vacancy-interstitial pairs

are in

_higher

concentration in these

phases

than in usual

solides,

moreover

_they

form linear defects extended over ten to fifteen molecular

_layers.

The internal structure of these defects is reminiscent of that of GP _zones, which are

_responsible

for the structural

_hardening

of aluminium

_alloys.

_However,

in SmB and G the orientational disorder of molecules around their

_long

axis may be at the

_origin

of the

_high

vacancy

concentration. It appears that this concentration is rather

independent

of the

_sample

nature

and

_preparation

and that even several

_days

of

_annealing

in the

_mesophase

temperature

range

seem to have no influence on the

_{scattering strength}

of the

_{samples. Owing}

to the known

dynamical properties

of such rotational motions the

_{vacancy-interstitial pairs}

are

_likely

to be

fairly

mobile.

_Consequently

the mechanical

_properties

of these materials may be rather insensitive to these defects in the low

_frequency

_limit,

while thermal

_{phonons couple easily}

to

them.

Besides an

_improvement

in the

_description

of the linear

_defects,

our data

analyses

have also

brought

to our attention the

_existence,

for

_asymmetrical

_molecules,

of a second class of

_purely

displacive

linear defects

_{corresponding}

to a local

_ordering

of the

_long

molecular axes. Let us

remark that the very few SmB

phases

of

polar

molecules seem to behave

_differently

since the

1525

walls,

typical

of the smectic

_phases

of

_{polar compounds}

_[18].

_Obviously,

a

_{precise description}

of the

_organisation

in Smectics B and G based on

_X-ray

diffraction data cannot be obtained

without an

analysis

of the whole diffraction

_pattern,

since the fluctuations take a

_great

_part in

the

_organisation

and cannot be considered as small

perturbations.

Nevertheless,

the methods

currently

used in the

_study

of a

_{single crystal}

can

_help

us to estimate the different kinds of

fluctuations. In the

_light

of this

evaluation, it appears that the SmB and

SmG

_phases

present

paradoxical properties.

The occurrence of localized

_point

defects is

_typical

of a

_crystalline

solid ;

the main

_part

of the molecular disorder is rather orientational than translational and this is a characteristic

_property

of

_{plastic crystals.}

However the

_{smectogenic (or lamellar)}

properties

of such

_systems

are related to the

anisotropy

of the molecule

_together

with the conformational disorder of the

_{aliphatic chains}

_[9].

At

least,

in smectics

B,

the lamellar

structure is

_{supported by}

the

_large

amount of

_stacking

faults

[20].

In the

_opposite

way, some

SmG

_phases

_present

a lot of

_{sharp Bragg}

_{peaks imaging}

a rather

_perfect

3D lattice. However since most of fluctuations are found in both SmB and G

phases, they

have to be considered in the same way,

they

both

_belong

to a class of

orientationally

disordered

crystals

of

mesogenic

molecules.

Acknowledgments.

_

I am _very

_grateful

to Professor A. Guinier for fruitful

discussions,

Mr. A. Saint-Martin has made

_{perfect copies}

of the

_original

_X-ray

diffraction

patterns.

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Phases

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Scientific,

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